Mass spectrometers are used to determine the chemical identity of substances by determining the mass of ions derived from the substances. The mass of an ion is determined by using the known behavior of charged particles in electric and magnetic fields, with some characteristic of the ion trajectory being observed and used to deduce the mass-to-charge ratio of the ion. Mass spectrometers may be divided into two broad classes: instruments that produce a beam of ions to effect mass analysis (such as magnetic sector spectrometers and quadrupole spectrometers) and instruments that trap a population of ions to effect mass analysis (such as ion cyclotron resonance mass spectrometers and Paul ion trap mass spectrometers).
The various types of mass spectrometers have advantages and disadvantages, and a large variety of instruments are now commercially available. No one type of instrument can deliver the necessary performance in all types of applications at an acceptable cost, and vigorous competition exists between the manufacturers of the various types of instruments to increase performance while controlling cost.
One disadvantage of trap-type mass spectrometers, either the Paul ion trap mass spectrometer or the ion cyclotron resonance mass spectrometer (ICR), is that the presence of the population of ions necessarily perturbs the electric field experienced by the ions, so that the ion trajectories depend on the number of ions present. This results in inaccuracy in the determination of m/z, because the field perturbation is quite complex, and the number of ions may change during mass analysis. The "space charge" introduced by the ions limits the number of ions that may be present during mass analysis if mass accuracy (and mass resolution) are to be maintained. For the Paul ion trap mass spectrometer, the practical effect of space charge is that the dynamic range (for purposes of mass analysis) is limited to about two orders of magnitude, because the more abundant ions "fill" the trap before the population of non-abundant ions is great enough to be detected with an adequate signal-to-noise ratio.
This limitation is most severe in those applications where the amount of analyte varies widely and unpredictably, such as in the gas chromatographic/mass spectrometric investigation of samples encountered in environmental analysis. Because of the costly high-field electromagnets needed for ion cyclotron resonance spectrometers, these instruments have seen little commercial use as detectors in chromatographic instruments for which the detector must be relatively inexpensive. In contrast, Paul ion trap mass spectrometers are now used almost exclusively as GC detectors, so the space charge limitation to dynamic range, although important to both types of spectrometer, is of more practical importance in Paul ion trap mass spectrometers.
An important development in the use of the Paul ion trap as a chromatographic detector was the dynamic control of the number of ions stored in the trap by adjusting the length of time during which ions are formed. U.S. Pat. No. 5,107,109 describes a method wherein a preliminary analysis is performed to estimate the rate of ion formation, and the actual mass analysis is then accomplished by using an ionization interval (calculated from the rate of ion formation) that gives a fixed, "target" number of ions in the trap. For well-separated chromatographic peaks, this dynamic control of the ionization time can extend the dynamic range so that analytes of concentrations varying by as much as five orders of magnitude can be successfully mass-analyzed. However, if the compounds are not chromatographically resolved, dynamic control of the ionization time will allow the acquisition of the mass spectrum of the mixture of the two compounds, but the internal dynamic range of the mass spectrum is limited to two orders of magnitude, and the less abundant compound may not be observed at all.
Another method of controlling the extent of space charge is the selective exclusion of ions from the trap, either during or after the formation of ions. From the time of the first commercial introduction of the Paul ion trap mass spectrometer, the r.f. voltage during ionization was adjusted so that certain low-mass ions (from air, water, etc.) would not be stored during ionization. Dawson and coworkers used a combined DC and r.f. field during ionization that allowed only a narrow mass range to be stored. March and coworkers (M. A. Armitage, J. E. Fulford, D. -N. Hoa, R. J. Hughes and R. E. March, "The Application of Resonant Ion Ejection to Quadrupole Ion Storage Mass Spectrometry: A Study of Ion/Molecule Reactions in the QUISTOR," 1979, Can. J. Chem., vol. 57, pp. 2108-2113) used resonance ejection to selectively eliminate ions from the trap. Use of alternating steps of ionization and ejection of undesired ions through the use of a DC field is described by Weber-Grabau (U.S. Pat. No. 4,818,869). Franzen et al. (European patent application, publication 0362432) describe the use of broadband waveforms for the resonance ejection of undesired ions during ionization.
The use of broadband waveforms for the ejection of ions from the ion cyclotron resonance trap is well established, although this has mostly been done for purposes other than simply controlling space charge, such as ion isolation prior to an ms/ms experiment. The early workers used noise waveforms (generated by analog methods) for ion ejection, but Marshall et al. (U.S. Pat. No. 4,761,545) describe calculated waveforms tailored to the particular experiment. In Marshall et al., a table of numbers is stored in a digital memory and these points are sequentially converted to an analog voltage by a digital-to-analog converter and associated electronic circuits. The "arbitrary waveform" was calculated by Marshall et al. by first choosing the desired frequency spectrum of the waveform and then using the inverse Fourier transform to calculate the waveform having the desired frequency spectrum. This technique of calculating a waveform using the inverse Fourier transform (inverse FT or FFT for "fast Fourier transform") and then creating the waveform by successively converting to analog form the digital values in a stored table is called the SWIFT method (for Stored Waveform Inverse Fourier Transform).
Formally, the Fourier transform maps a complex function to a complex function. Practically, a waveform is a pure real function (amplitude as a function of time) which is called the "time domain", and the Fourier transform maps this to a complex function (a complex quantity as a function of frequency) which is called the "frequency domain". The inverse Fourier transform maps the complex function to the time domain and the discrete inverse Fourier transform (used for numerical computation) acts on an array of complex data. Each point in the array may be described using the cartesian representation (with a real and an imaginary part) or equivalently by using the polar representation (with a magnitude and a phase part), but algorithms for calculating the forward and inverse discrete Fourier transform generally use the cartesian representation. The polar representation has the advantage that the magnitude and phase parts are closely related to the familiar parameters of simple cosine waves: the magnitude part of the frequency spectrum at a particular frequency corresponds to the amplitude of the cosine function associated with that frequency, and the phase part of the frequency spectrum at that frequency corresponds to the phase of the cosine function. For a particular application of Marshall's method, the magnitude part of the frequency spectrum is assigned according to the efficiency with which ions are to be ejected; in a typical application the magnitude would be a constant for those frequencies associated with ions that are to be ejected, the magnitude would be zero for some range of frequencies associated with ions that are to be retained within the cell, and the magnitude would likewise be zero for frequencies outside the range of possible ion frequencies.
The phase part of the frequency spectrum is more difficult to assign, because there is no single, simple criterion that unambiguously leads to a phase assignment. For a given assignment of the magnitude part of the frequency spectrum, each possible assignment of the phase part of the frequency spectrum governs the time course of the resulting time domain waveform that results from the inverse Fourier transform. Marshall et al. noted that for the simple, useful magnitude assignment in which the magnitude is everywhere zero, except for a range of frequencies at which it is constant, the simplest conceivable phase assignment of zero at all frequencies results in a time domain waveform that is essentially a very narrow pulse. These workers rejected this phase assignment because the high amplitude during the pulse results in the need for excessive dynamic range in both the analog and digital parts of the electronic hardware needed to produce the waveform. They recommended the assignment of the phase as a quadratic function of the frequency; the resulting time domain waveform is not pulse-like, but has the power distributed throughout the time period so that the dynamic range requirements of the electronics are much less demanding. More recently, Goodman et al. (U.S. Pat. No. 4,945,234) and Guan et al. (U.S. Pat. No. 5,013,912) have further developed methods for assigning the phase part of the frequency spectrum.
That the ion motions in ICR traps and Paul traps share enough characteristics that the waveforms used for ion ejection are much the same in both instruments has been recognized since the work of Marshall et al., who described the SWIFT technique for both traps. In the ICR trap the ion trajectories are circular, but the excitation voltage is applied between opposing plates and the motion in the coordinate normal to the plates is sinusoidal, with the frequency of the motion being inversely proportional to the m/z of the ion. In the Paul trap, the excitation voltage is applied between the two end cap electrodes, while the ion motion is a reciprocating motion between the two electrodes. Over a large range of useful operating conditions the reciprocating motion may be approximated as being sinusoidal, with a frequency that is inversely proportional to the m/z of the ion. For both traps (within the limits of this approximation), the response of the ions to an excitation voltage is described by the linear, inhomogeneous differential equation commonly described as the equation of forced harmonic motion. Thus, much the same waveforms may be used in both Paul traps and ICR traps, and theoretical as well as practical considerations are shared in the development of waveforms for the two types of instrument. Guan and Marshall have described in some detail the relationship between the theories of ion ejection in the Paul trap and the ICR trap (Anal. Chem. 65, 1288-1294 (1993)).
Recently Kelley described the use of noise waveforms for the isolation of ions of a narrow mass range in the Paul ion trap (U.S. Pat. No. 5,134,286). He described the application of a frequency band-reject filter to a noise waveform so that the resulting waveform would cause all ions with resonant frequencies other than those within a specified band to be ejected from the trap. Kelley did not specify whether the noise waveform was created with an analog noise generator or with a digital arbitrary waveform generator.
When attempting to apply the previously described methods (e.g. the methods of Marshall, Franzen and Kelley) to the problem of selectively ejecting ions during the ionization stage in a Paul trap, we found serious limitations in all the calculated waveforms. The important problem of excluding ions from the Paul trap during the ionization interval has not previously been adequately investigated. In ICR spectrometry, the ion exclusion has generally been performed after ionization. The requirements imposed on such waveforms are less stringent than those that are needed of waveforms that exclude ions during ionization; in particular, the frequency content of the waveform must stay uniform throughout the ionization period because ions are formed throughout the ionization period. For example, a linear scan (or at least a monotonic scan) of the resonance ejection frequency is commonly used to exclude ions from an ICR cell, but such a waveform would not be suitable for ejection during ionization, because ions created after the frequency has swept past the resonance frequency would not be ejected.